Titlebook: Applied Number Theory; Harald Niederreiter,Arne Winterhof Textbook 2015 Springer International Publishing Switzerland 2015 coding theory.c

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A Review of Number Theory and Algebra, brief review of this theory for those who already have some background on number theory and a crash course on elementary number theory for those who have not. Apart from trying to be friendly, we also follow good practice when we prepare the ground for the coming attractions by collecting some basi

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Cryptography,years as it was already used in one form or other in the ancient civilizations of Egypt, Mesopotamia, China, Greece, and Rome. It would lead us too far astray if we were to delineate the colorful history of cryptology here, but we will occasionally mention some tidbits. A systematic account of the h

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Coding Theory, you commit and thus increase the quality of your life. There is probably no panacea for all human errors and mishaps, but in the setting of communication technology, number theory and finite fields can help to prevent errors and ensure the quality of communication. The aim of this chapter is to exp

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Quasi-Monte Carlo Methods,re taught that a definite integral . is evaluated by the fundamental theorem of integral calculus which says that . where the function . is an antiderivative of the integrand .. What you are often not told is that there are many cases where . cannot be expressed in finite terms by means of elementar

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Pseudorandom Numbers,uce random samples. Maybe we were wise to keep quiet, because nobody really knows how to generate honest-to-goodness random samples in practice. On the other hand, the purely theoretical framework for random sampling is clear: we have a set with at least two elements, we are given a probability dist

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Further Applications,s are the more colorful birds. Just like error-correcting codes, check-digit systems help to eliminate errors in data, but their aims are more modest than those of error-correcting codes. In a check-digit system we extend an identification number, as for example a bank account number, by a control s